Translation:We split up.
I tried to google your question, and perhaps you may be right actually, "נפרדנו" is the best translation of "separated". I don't have a clear answer, I can just tell you how it sounds to me as a native speaker: "נפרדנו" means that we were together until at some point we decided to split up. In Hebrew we also use "נפרדנו" as "we broke up" (we were in romantic relationship, and now we don't anymore). "We were separated" sounds like we didn't have any connection for a long period of time, and maybe somebody forced us to be separated. You can say this even about two people that didn't even knew each other at the time.
I see where you're coming from. The difference is really small, but I just need to know if I can use that word in a passive sense. Technically, if two people decided to separate, they were separated. More context would bear out whether they did it or someone else did. As far as I can tell, you say that Israelis use this word in an active sense, but can it also be passive?
My guess is that it is passive because it is nif'al, but as all languages do, Hebrew changed as people used the word in an active way.
Just a guess.
Thanks for you help by the way, you have been very helpful on more than one occasion.